Existence result of global solutions for a class of generic reaction diffusion systems

[1] A. Aarab, N. Alaa and H. Khalfi, Generic reaction diffusion model with application to image restoration and
enhancement, Elect. J. Diff. Eq. 125 (2018) 1–12.
[2] N. Alaa and M. Zirhem, Bio-inspired reaction diffusion system applied to image restoration, Int. J. Bio-Inspired
Comput. 12(2) (2018) 128–137.
[3] N. Alaa, M. Ait Oussous and Y. Ait Khouya, Anisotropic and nonlinear diffusion applied to image enhancement
and edge detection, Int. J. Computer Appl. Tech. 49(2) (2014) 122–133.
[4] N. Alaa, M. Ait Oussous, W. Bouarifi and D. Bensikaddour, Image restoration using a reaction diffusion process,
Elect. J. Diff. Eq. 197 (2014) 1–12.
[5] L. Alvarez, F. Guichard, P.L. Lions and J.M. Morel, Axioms and fundamental equations of image processing,
Arch. Rational Mech. Anal. 123 (1993) 199–257.
[6] L. Alvarez, P.L. Lions and J.M. Morel, Image selective smoothing and edge detection by nonlinear diffusion II,
SIAM J. Numerical Anal. 29(3) (1992) 845–866.
[7] H. Amann, Dynamic theory of quasilinear parabolic equations, ii. reaction diffusion systems, Differential Integral
Equations Vol. 3 (1990), no. 1, 13–75.
[8] P. Benilan and H. Brezis, Solutions faibles d’´equations d’´evolution dans les espaces de Hilbert, Ann. Inst. Fourier
(Grenoble), Tome 22(2) (1972) 311–329.
[9] F. Catt´e, P.L. Lions, J.M. Morel and T. Coll, Image selective smoothing and edge detection by nonlinear diffusion,
SIAM J. Numerical Anal. 29(1) (1992) 182–193.
[10] W.S. Du and Th. M. Rassias, Simultaneous generalizations of known fixed point theorems for a Meir-Keeler type
condition with applications, Int. J. Nonlinear Anal. Appl. 11(1) (2020) 55–66.
[11] J. Fr¨ohlich and J. Weicker, Image Processing Using a Wavelet Algorithm for Nonlinear Diffusion, Report 104,
Laboratory of Technomathematics, University of Kaiserslautern, Kaiserslautern, 1994.
[12] S.M.R. Hashemi, H. Hassanpour, E. Kozegar and T. Tan, Cystoscopic Image Classi cation Based on Combining
MLP and GA, Int. J. Nonlinear Anal. Appl. 11(1) (2020) 93–105.[13] S.M.R. Hashemi, H. Hassanpour, E. Kozegar and T. Tan, Cystoscopy image classification using deep convolutional
neural networks, Int. J. Nonlinear Anal. Appl. 10(1) (2019) 193–215.
[14] S. Kant and V. Kumar, Dynamical behavior of a stage structured prey-predator model, Int. J. Nonlinear Anal.
Appl. 7(1) (2016) 231–241.
[15] O.A. Ladyzhenskaya, V.A. Solonnikov and N.N. Ural’tseva, Lineinye i Kvazilineinye Uravneniya Parabolicheskogo
Tipa (Linear and Quasi-Linear Equations of Parabolic Type), Moscow, Nauka, 1967.
[16] J.L. Lions, Equations Diff´erentielles Operationnelles et Probl`emes aux Limites, vol. 111, Springer-Verlag, 2013.
[17] S. Mesbahi and N. Alaa, Mathematical analysis of a reaction diffusion model for image restoration, Ann. Univ.
Craiova, Math. Comp. Sci. Ser. 42(1) (2015) 70–79.
[18] S. Morfu, On some applications of diffusion processes for image processing, Phys. Lett. A 373(29) (2009) 24–44.
[19] J.D. Murray, Mathematical Biology I : An Introduction, Volume I, Springer-Verlag, 3rd edition, 2003.
[20] J.D. Murray, Mathematical Biology II : Spatial Models and Biochemical Applications, volume II, Springer-Verlag,
3rd edition, 2003.
[21] V. Pata, Fixed Point Theorems and Applications, Springer, 2019.
[22] M. Pierre, Global existence in reaction diffusion systems with dissipation of mass: a survey, Milan J. Math. 78(2)
(2010) 417–455.
[23] P. Quittner and P. Souplet, Superlinear Parabolic Problems: Blow-up, Global Existence and Steady States, 2nd
ed., Springer, Birkh¨auser, 2019.
[24] D. Schmitt, Existence Globale ou Explosion Pour les Systemes De r´eaction-Diffusion Avec Contrˆole de Masse,
Ph.D. thesis, Nancy 1, 1995.
[25] J. Simon, Compact sets in the space L
p
(0, T, B), Ann. Math. Pura Appl. 146 (1986) 65–96.
[26] J. Weicker, Efficient image segmentation using partial differential equations and morphology, Pattern Recog. 34(9)
(2001) 1813-1824.
[27] J. Weicker and C. Schn¨orr, PDE-based preprocessing of medical images. Kunstliche Intelligenz, 3 (2000) 5–10.
[28] J. Weicker, Anisotropic Diffusion in Image Processing, PhD thesis, Universit¨at Kaiserslautern, Kaiserslautern,
Germany, 1996.
[29] S. Xu, S. Chenb and S. Aleksi´c, Fixed point theorems for generalized quasi-contractions in cone b-metric spaces
over Banach algebras without the assumption of normality with applications, Int. J. Nonlinear Anal. Appl. 8(2)
(2017) 335–353.